1. Field of the Invention
The present invention relates to a correction method for correcting electrical characteristics of electronic components measured by an actual measuring system with measured results, which do not agree with a reference measuring system, to electrical characteristics assumed to be obtained by the reference measuring system; a quality checking method using the correction method for electronic components; and a characteristic measuring system for performing the correction method on electronic components.
2. Description of the Related Art
In measuring electrical characteristics of electronic components, sometimes, the same electronic component or the same kind thereof is measured by a plurality of measuring systems, such as a measuring system set up in a site for an electronic component manufacturer and another measuring system set up in a site for a user of the electronic components.
Because measurement errors are different from those in each measuring system in such a case, the precision of measurement reproducibility is low, so that a problem arises from inconsistency of measured results for the same electronic component or the same kind thereof.
Such measurement errors are comparatively low in the electrical characteristic measurement in a low frequency region, so that there is not much problem on this point. Whereas, in a high frequency region of 100 MHz or more, the measurement errors between measuring systems are large, so that in order to improve the precision of measurement reproducibility, calibration using an absolute correction method is performed especially in a high frequency region of several GHz or more.
A standard device is prepared in advance in that an instrument having a target electrical characteristic precisely identified, such as an open/short/load/through, an example of which is the model 85052B manufactured by Agilent Technologies Company. Various measurements of this standard device by each measuring system identify the error factor of each measuring system. Then, the calibration such as a high-accuracy full two-port correction method is performed thereon to eliminate the identified error factor, improving the precision of measurement reproducibility (such a correction method is referred to as an absolute correction method below).
In such a manner, a measuring system can improve the precision of measurement reproducibility by performing the high-accuracy calibration using the standard device mentioned above. However, such calibration can be performed on only an electronic component with a coaxial form (referred to as a coaxial-type electronic component below) so as to measure precisely.
Whereas, the calibration mentioned above has been difficult to perform on an electronic component with a non-coaxial form (referred to as a noncoaxial-type electronic component below). The reason thereof is described below.
A standard device for noncoaxial-type electronic components is extremely difficult to be manufactured to have substantially the same performance as that for coaxial-type electronic components, and manufacturing cost for such a standard device becomes extremely large. Moreover, even if the standard device is manufactured, it is difficult to specify electrical characteristics thereof in high accuracy.
Furthermore, even if a standard device for noncoaxial-type electronic components is prepared, in a measuring system capable of performing the high-accuracy calibration (such as the full two-port correction method), the standard device capable of performing the calibration mentioned above is limited to the instrument to achieve the value (typically, the open/short/load/through), which cannot be achieved unless the component is of a coaxial-type. By such reasons, the calibration mentioned above is difficult to be performed on noncoaxial-type electronic components.
In performing a TRL correction method, a kind of calibration, a standard device (typically, a standard device of a through/reflection/line) for noncoaxial-type electronic components such as waveguides and microstrip lines may be easily manufactured. However, even in the standard device suitable for the TRL correction method, it is difficult to specify electrical characteristics thereof in high accuracy.
As described above, in the measurement of electrical characteristics of noncoaxial-type electronic components, it is difficult to improve measurement accuracy by performing the calibration thereon based on the absolute correction method. Therefore, up to now, in the measurement of electrical characteristics of noncoaxial-type electronic components, the calibration at junction points of the electronic component is not performed but the measurement is performed in a state of being attached to a measurement fixture, as will be described below.
A measurement fixture is prepared, which has coaxial input-output terminals for a measuring system while having noncoaxial input-output terminals for a noncoaxial-type electronic component. This measurement fixture is electrically connected to a piece of coaxial cable, which is connected to input-output terminals of the measuring system. Then, the noncoaxial-type electronic component is mounted on the measuring system so that electrical characteristics of the component are measured. In addition, it is preferable that the calibration such as a full two-port correction method be performed on the coaxial cable connected to the input-output terminals of the measuring system up to the tip end.
In such an electrical characteristic measurement method for noncoaxial-type electronic components using the measurement fixture, calibration cannot be performed by including the measurement fixture. Therefore, the reproducibility of measured results is low. In order to increase the reproducibility of the measured results, the following adjustments of the measuring system are performed.
In this adjustment, one measuring system is regarded as a reference measuring system having a reference measurement fixture and the other is regarded as an actually measuring system having an actual measurement fixture, so that the actual measurement fixture of the actually measuring system is adjusted so as to bring the measured result from the actually measuring system to that from the reference measuring system. Specifically, electrical characteristics of an arbitrary sample (electronic component) are measured by the reference measuring system; electrical characteristics of the same sample are measured by the actually measuring system, and then, the actual measurement fixture is adjusted so that both the measured results are equalized. The adjustment is specifically performed as follows.
The actual measurement fixture is arranged that a coaxial connector to be connected to a measuring system is attached to a printed circuit board having input-output terminals to be connected to a sample, which are disposed at a wiring end-portion on the substrate surface. In the actual measurement fixture structured as above, adjustment is performed as follows. While part of printed wiring on the printed circuit board being cut off, or solder being put on the printed wiring, changes in the measured results are measured, and the treatment is finalized after the same electrical characteristics as those of the measured results in the reference measuring system are obtained.
The measuring method of electrical characteristics of electronic components described above has the following problems for both measurements of coaxial-type electronic components and noncoaxial-type electronic components.
In measuring method of coaxial-type electronic components, although the reference device necessary for the calibration is available, it is expensive, so that there is a problem that the cost of the calibration is increased, and by extension, the cost for measuring electrical characteristics of electronic components is increased.
In measuring method of noncoaxial-type electronic components, because the adjustment method of the actual measurement fixture mentioned above is not theoretically clarified but is depending on skills and hunch and taking a lot of trouble, it is difficult to reproduce the adjustment in high accuracy even to the old hand.
Furthermore, such an adjustment method of the actual measurement fixture is a method only capable of assuring the reproducibility when measuring the sample used in the adjustment, and when another sample is measured, the reproducibility is not always assured, so that it would have to say that the reproducibility be unstable.
Accordingly, it is a principal object of the present invention to provide a correction method of measurement errors in that measured results of actual measurement, which do not perfectly agree with a reference measuring system, is corrected to the same level of measured results by the reference measuring system.
In order to achieve the object mentioned above, a measurement-error correction method, in which after electrical characteristics of a target electronic component are measured by an actual measuring system with measured results that do not agree with a reference measuring system, the measured value is corrected to electrical characteristics assumed to be obtained by the reference measuring system, the measurement-error correction method comprising the steps of preparing a correction-data acquisition sample in advance, which generates the same electrical characteristics as arbitrary electrical characteristics of the target electronic component by measurement operation; measuring electrical characteristics of the correction-data acquisition sample by the reference measuring system and the actual measuring system, respectively; obtaining an interrelating formula between results measured by the reference measuring system and results measured by the actual measuring system; and correcting electrical characteristics of the target electronic component to electrical characteristics assumed to be obtained by the reference measuring system by substituting the electrical characteristics of the target electronic component measured by the actual measuring system in the interrelating formula for computation. Thereby the following functions are provided.
Based on the measured results of the correction-data acquisition sample with not-identified electrical characteristics, the interrelating formula between the actual measuring system and the reference measuring system is obtained. Then, electrical characteristics of the target electronic component are corrected to the electrical characteristics assumed to be obtained by the reference measuring system on the basis of the interrelating formula, eliminating calibration using an expensive authentic sample and adjustment of measurement fixtures. Moreover, the electrical characteristic correction is performed by theoretical computation, so that repeatability of electrical characteristic measurement of electronic components with any shapes (coaxial or noncoaxial shape) can be increased.
The present invention proposes an analytical relative correction method and an approximate-relative correction method as correction methods using the interrelating formula.
For obtaining the interrelation equation by the analytical relative correction method, the present invention may comprise the procedures of creating a theoretical equation for obtaining a measurement true value of the actual measuring system in the signal transfer pattern and a theoretical equation for obtaining a measurement true value of the reference measuring system in the signal transfer pattern, respectively; creating the interrelating formula comprising an arithmetic expression, which includes an undetermined coefficient and directly and exclusively shows the relationship between the measurement true value of the actual measuring system and the measurement true value of the reference measuring system, based on both the theoretical equations; measuring electrical characteristics of the correction-data acquisition sample by the reference measuring system and the actual measuring system, respectively; and identifying the undetermined coefficient by substituting the electrical characteristics of the correction-data acquisition sample measured by both the measuring systems in the interrelating formula.
For obtaining the interrelation equation by the approximate-relative correction method, the present invention may comprise the procedures of creating the interrelating formula comprising an expression of degree n (n is a natural number) including an undetermined coefficient and approximately showing the relationship between the value measured by the actual measuring system and the value measured by the reference measuring system, measuring electrical characteristics of the correction-data acquisition sample by the reference measuring system and the actual measuring system, respectively, and identifying the undetermined coefficient by creating an undetermined-coefficient computing equation based on the interrelating formula so as to substitute the electrical characteristics of the correction-data acquisition sample measured by both the measuring systems in the undetermined-coefficient computing equation.
Preferably, measurement-error correction is performed on a plurality of electrical characteristics which are included in the target electronic component. In this connection, a plurality of samples having electrical characteristics which are different from each other as measured by the measuring system are used as the correction-data acquisition sample. Thereby, accuracy of correction by the interrelation equation is further improved. Moreover, it is enough to prepare the correction-data acquisition samples having arbitrary electrical characteristics without identifying a physical true value of the characteristics, simplifying manufacturing or availability.
Preferably, a characteristic of measurement-error correction is an S parameter and a measuring instrument constituting the measuring system is a network analyzer.
Examples of the S parameter may be a reflection coefficient in a forward direction, transfer coefficient in the forward direction, reflection coefficient in a backward direction, and transfer coefficient in the backward direction.
Specific procedures of creating the interrelating formula by the approximate-relative correction method are shown as follows.
The method for creating the interrelating formula comprises the steps of:
creating the following interrelating formula (B2) comprising a linear expression and the following undetermined coefficient computing equations (B1a) to (B1d);
preparing five correction-data acquisition samples with electrical characteristics, which are generated by measurement operation of the measuring system and being different from each other, and then measuring S parameter (S11n, S21n, S12n, and S22n:n: natural numbers of 1 to 5) of the correction-data acquisition samples by the reference measuring system and the actual measuring system;
determining undetermined coefficients (am, bm, cm, and dm: m; integers of 0 to 4) by substituting the measured S parameter (S11n, S21n, S12n, and S22n) in the undetermined coefficient computing equations (B1a) to (B1d); and
inserting the identified undetermined coefficients (am, bm, cm, and dm) into the interrelating formula (B2).                     [                  Numerical          ⁢                      xe2x80x83                    ⁢          Formula          ⁢                      xe2x80x83                    ⁢          1                ]                            xe2x80x83                                          (                                                                      S                  11                                      1                    *                                                                                                                        S                  11                                      2                    *                                                                                                                        S                  11                                      3                    *                                                                                                                        S                  11                                      4                    *                                                                                                                        S                  11                                      5                    *                                                                                )                =                              (                                                                                S                    11                                          1                      ⁢                      M                                                                                                            S                    21                                          1                      ⁢                      M                                                                                                            S                    12                                          1                      ⁢                      M                                                                                                            S                    22                                          1                      ⁢                      M                                                                                        1                                                                                                  S                    11                                          2                      ⁢                      M                                                                                                            S                    21                                          2                      ⁢                      M                                                                                                            S                    12                                          2                      ⁢                      M                                                                                                            S                    22                                          2                      ⁢                      M                                                                                        1                                                                                                  S                    11                                          3                      ⁢                      M                                                                                                            S                    21                                          3                      ⁢                      M                                                                                                            S                    12                                          3                      ⁢                      M                                                                                                            S                    22                                          3                      ⁢                      M                                                                                        1                                                                                                  S                    11                                          4                      ⁢                      M                                                                                                            S                    21                                          4                      ⁢                      M                                                                                                            S                    12                                          4                      ⁢                      M                                                                                                            S                    22  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B1a                                    (                                                                      S                  21                                      1                    *                                                                                                                        S                  21                                      2                    *                                                                                                                        S                  21                                      3                    *                                                                                                                        S                  21                                      4                    *                                                                                                                        S                  21                                      5                    *      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                                                              1                                                                                                  S                    11                                          2                      ⁢                      M                                                                                                            S                    21                                          2                      ⁢                      M                                                                                                            S                    12                                          2                      ⁢                      M                                                                                                            S                    22                                          2                      ⁢                      M                                                                                        1                                                                                                  S                    11                                          3                      ⁢                      M                                                                                                            S                    21                                          3                      ⁢                      M                                                                                                            S                    12                                          3                      ⁢                      M                                                                                                            S                    22                                          3                      ⁢                      M                                                                                        1                     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                                   S                    11                                          5                      ⁢                      M                                                                                                            S                    21                                          5                      ⁢                      M                                                                                                            S                    12                                          5                      ⁢                      M                                                                                                            S                    22                                          5                      ⁢                      M                                                                                        1                                                      )                    ⁢                      (                                                                                b                    1                                                                                                                    b                    2                                                                                                                    b                    3                                                                                                                    b                    4                                                                                                                    b                    0                                                                        )                                      B1b                                    (                                                                      S                  12                                      1                    *                                                   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                                                       S                    21                                          4                      ⁢                      M                                                                                                            S                    12                                          4                      ⁢                      M                                                                                                            S                    22                                          4                      ⁢                      M                                                                                        1                                                                                                  S                    11                                          5                      ⁢                      M                                                                                                            S                    21                                          5                      ⁢                      M                                                                                                            S                    12                                          5                      ⁢                      M                                                                                                            S                    22                                          5                      ⁢                      M                                                                                        1                                                      )                    ⁢                      (                                                                                c                    1                                                                                                                    c                    2                                                                                                                    c                    3                                                                                                                    c                    4                                                                                                                    c                    0                                                                        )                                      B1c                                    (                                                                      S                  22                                      1                    *                                                                                                                        S                  22                                      2                    *                                                                                                                        S                  22                                      3                    *                                                                                                                        S                  22                                      4                    *                                                                                                                        S                  22                                      5                    *                                                                                )                =                              (                                                                                S                    11                                          1                      ⁢                      M                                                                                                            S                    21                                          1                      ⁢                      M                                                                                                            S                    12                                          1                      ⁢                      M                                                                                                            S                    22                                          1                      ⁢                      M                                                                                        1                                                                                                  S                    11                                          2                      ⁢                      M                                                                                                            S                    21                                          2                      ⁢                      M                                                                                                            S                    12                                          2                      ⁢                      M                                                                                                            S                    22                                          2                      ⁢                      M                                                                                        1                                                                                                  S                    11                                          3                      ⁢                      M                                                                                                            S                    21                                          3                      ⁢                      M                                                                                                            S                    12                                          3                      ⁢                      M                                                                                                            S                    22                                          3                      ⁢                      M                                                                                        1                                                                                                  S                    11                                          4                      ⁢                      M                                                                                                            S                    21                                          4                      ⁢                      M                                                                                                            S                    12                                          4                      ⁢                      M                                                                                                            S                    22                                          4                      ⁢                      M                                                                                        1                                                                                                  S                    11                                          5                      ⁢                      M                                                                                                            S                    21                                          5                      ⁢                      M                                                                                                            S                    12                                          5                      ⁢                      M                                                                                                            S                    22                                          5                      ⁢                      M                                                                                        1                                                      )                    ⁢                      (                                                                                d                    1                                                                                                                    d                    2                                                                                                                    d                    3                                                                                                                    d                    4                                                                                                                    d                    0                                                                        )                                      B1d      
S11n*, S21n*, S12n*, and S22n*: the S parameter of the correction-data acquisition samples measured by the reference measuring system
S11nM, S21nM, S12nm, and S22nM: the S parameter of the correction-data acquisition samples measured by the actual measuring system                     [                  Numerical          ⁢                      xe2x80x83                    ⁢          Formula          ⁢                      xe2x80x83                    ⁢          2                ]                            xe2x80x83                                          (                                                                      S                  11                  *                                                                                                      S                  21                  *                                                                                                      S                  12                  *                                                                                                      S                  22                  *                                                              )                =                                            (                                                                                          a                      1                                                                                                  a                      2                                                                                                  a                      3                                                                                                  a                      4                                                                                                                                  b                      1                                                                                                  b                      2                                                                                                  b                      3                                                                                                  b                      4                                                                                                                                  c                      1                                                                                                  c                      2                                                                                                  c                      3                                                                                                  c                      4                                                                                                                                  d                      1                                                                                                  d                      2                                                                                                  d                      3                                                                                                  d                      4                                                                                  )                        ⁢                          (                                                                                          S                      11                      M                                                                                                                                  S                      21                      M                                                                                                                                  S                      12                      M                                                                                                                                  S                      22                      M                                                                                  )                                +                      (                                                                                a                    0                                                                                                                    b                    0                                                                                                                    c                    0                                                                                                                    d                    0                                                                        )                                      B2      
S11*, S21*, S12*, and S22*: the S parameter of the target electronic component assumed to be obtained by the reference measuring system
S11M, S21M, S12M, and S22M: the S parameter of the target electronic component measured by the actual measuring system
Other specific procedures of creating the interrelating formula by the approximate-relative correction method are further shown as follows.
The method for creating the interrelating formula comprises the steps of:
creating the following interrelating formulas (C2a) to (C2d) comprising a quadratic expression and the following undetermined coefficient computing equations (C1a) to (C1d);
preparing 15 correction-data acquisition samples with electrical characteristics, which are generated by measurement operation and being different from each other, and then measuring S parameter (S11p, S21p, S12p, and S22p: p: natural numbers of 1 to 15) of the correction-data acquisition samples by the reference measuring system and the actual measuring system;
determining undetermined coefficients (aq, bq, cq, and dq: q; integers of 0 to 14) by substituting the measured S parameter (S11p, S21p, S12p, and S22p) in the undetermined coefficient computing equations (C1a) to (C1d); and
inserting the identified undetermined coefficients (aq, bq, cq, and dq) into the interrelating formulas (C2a) to (C2d).                               xe2x80x83                ⁢                              [                          Numerical              ⁢                              xe2x80x83                            ⁢              Formula              ⁢                              xe2x80x83                            ⁢              3                        ]                    ⁢                      xe2x80x83                    ⁢          C1a                                                  (                                                                      S                  11                                      1                    *                                                                                                                        S                  11                                      2                    *                                           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                  4                        ⁢                        M                                                              ⁢                                          S                      22                                              4                        ⁢                        M                                                                                                                                                        S                      12                                              4                        ⁢                        M                                                              ⁢                                          S                      22                                              4                        ⁢                        M                                                                                                              1                                                                                             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 S                      11                                              5                        ⁢                        M                                                              ⁢                                          S                      12                                              5                        ⁢                        M                                                                                                                                                        S                      11                                              5                        ⁢                        M                                                              ⁢                                          S                      22                                              5                        ⁢                        M                                                                                                                                                      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       ⁢                                          S                      22                                              13                        ⁢                        M                                                                                                              1                                                                                                  S                    11                                          14                      ⁢                      M                                                                                                            S                    21                                          14                      ⁢                      M                                                                                                            S                    12                                          14                      ⁢                      M                                                                                                            S                    22                                          14                      ⁢                      M                                                                                                                                  (                                              S                        11                                                  14                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        21                                                  14                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        12                                                  14                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        22                                                  14                          ⁢                          M                                                                    )                                        2                                                                                                              S                      11                                              14                        ⁢                        M                                                              ⁢                                          S                      21                                              14                        ⁢                        M                                                                                                                                                        S                      11                                              14                        ⁢                        M                                                              ⁢                                          S                      12                                              14                        ⁢                        M                                                                                                                                                        S                      11                                              14                        ⁢                        M                                                              ⁢                                          S                      22                                              14                        ⁢                        M                                                                                                                                                        S                      21                                              14                        ⁢                        M                                                              ⁢                                          S                      12                                              14                        ⁢                        M                                                                                                                                                        S                      21                                              14                        ⁢                        M                                                              ⁢                                          S                      22                                              14                        ⁢                        M                                                                                                                                                        S                      12                                              14                        ⁢                        M                                                              ⁢                                          S                      22                                              14                        ⁢                        M                                                                                                              1                                                                                                  S                    11                                          15                      ⁢                      M                                                                                                            S                    21                                          15                      ⁢                      M                                                                                                            S                    12                                          15                      ⁢                      M                                                                                                            S                    22                                          15                      ⁢                      M                                                                                                                                  (                                              S                        11                                                  15                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        21                                                  15                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        12                                                  15                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        22                                                  15                          ⁢                          M                                                                    )                                        2                                                                                                              S                      11                                              15                        ⁢                        M                                                              ⁢                                          S                      21                                              15                        ⁢                        M                                                                                                                                                        S                      11                                              15                        ⁢                        M                                                              ⁢                                          S                      12                                              15                        ⁢                        M                                                                                                                                                        S                      11                                              15                        ⁢                        M                                                              ⁢                                          S                      22                                              15                        ⁢                        M                                                                                                                                                        S                      21                                              15                        ⁢                        M                                                              ⁢                                          S                      12                                              15                        ⁢                        M                                                                                                                                                        S                      21                                              15                        ⁢                        M                                                              ⁢                                          S                      22                                              15                        ⁢                        M                                                                                                                                                        S                      12                                              15                        ⁢                        M                                                              ⁢                                          S                      22                                              15                        ⁢                        M                                                                                                              1                                                      )                    ⁢                      (                                                                                c                    1                                                                                                                    c                    2                                                                                                                    c                    3                                                                                                                    c                    4                                                                                                                    c                    5                                                                                                                    c                    6                                                                                                                    c                    7                                                                                                                    c                    8                                                                                                                    c                    9                                                                                                                    c                    10                                                                                                                    c                    11                                                                                                                    c                    12                                                                                                                    c                    13                                                                                                                    c                    14                                                                                                                    c                    0                                                                        )                                                            [                      Numerical            ⁢                          xe2x80x83                        ⁢            Formula            ⁢                          xe2x80x83                        ⁢            6                    ]                ⁢                  xe2x80x83                ⁢        C1d                                          (                                                                      S                  22                                      1                    *                                                                                                                        S                  22                                      2                    *                                                                                                                        S                  22                                      3                    *                                                                                                                        S                  22                                      4                    *                                                                                                                        S                  22                                      5                    *                                                                                                                        S                  22                                      6                    *                                                                                                                        S                  22                                      7                    *                                                                                                                        S                  22                                      8                    *                                                                                                                        S                  22                                      9                    *                                                                                                                        S                  22                                      10                    *                                                                                                                        S                  22                                      11                    *                                                                                                                        S                  22                                      12                    *                                                                                                                        S                  22                                      13                    *                                                                                                                        S                  22                                      14                    *                                                                                                                        S                  22                                      15                    *                                                                                )                =                              (                                                                                S                    11                                          1                      ⁢                      M                                                                                                            S                    21                                          1                      ⁢                      M                                                                                                            S                    12                                          1                      ⁢                      M                                                                                                            S                    22                                          1                      ⁢                      M                                                                                                                                  (                                              S                        11                                                  1                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        21                                                  1                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        12                                                  1                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        22                                                  1                          ⁢                          M                                                                    )                                        2                                                                                                              S                      11                                              1                        ⁢                        M                                                              ⁢                                          S                      21                                              1                        ⁢                        M                                                                                                                                                        S                      11                                              1                        ⁢                        M                                                              ⁢                                          S                      12                                              1                        ⁢                        M                                                                                                                                                        S                      11                                              1                        ⁢                        M                                                              ⁢                                          S                      22                                              1                        ⁢                        M                                                                                                                                                        S                      21                                              1                        ⁢                        M                                                              ⁢                                          S                      12                                              1                        ⁢                        M                                                                                                                                                        S                      21                                              1                        ⁢                        M                                                              ⁢                                          S                      22                                              1                        ⁢                        M                                                                                                                                                        S                      12                                              1                        ⁢                        M                                                              ⁢                                          S                      22                                              1                        ⁢                        M                                                                                                              1                                                                                                  S                    11                                          2                      ⁢                      M                                                                                                            S                    21                                          2                      ⁢                      M                                                                                                            S                    12                                          2                      ⁢                      M                                                                                                            S                    22                                          2                      ⁢                      M                                                                                                                                  (                                              S                        11                                                  2                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        21                                                  2                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        12                                                  2                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        22                                                  2                          ⁢                          M                                                                    )                                        2                                                                                                              S                      11                                              2                        ⁢                        M                                                              ⁢                                          S                      21                                              2                        ⁢                        M                                                                                                                                                        S                      11                                              2                        ⁢                        M                                                              ⁢                                          S                      12                                              2                        ⁢                        M                                                                                                                                                        S                      11                                              2                        ⁢                        M                                                              ⁢                                          S                      22                                              2                        ⁢                        M                                                                                                                                                        S                      21                                              2                        ⁢                        M                                                              ⁢                                          S                      12                                              2                        ⁢                        M                                                                                                                                                        S                      21                                              2                        ⁢                        M                                                              ⁢                                          S                      22                                              2                        ⁢                        M                                                                                                                                                        S                      12                                              2                        ⁢                        M                                                              ⁢                                          S                      22                                              2                        ⁢                        M                                                                                                              1                                                                                                  S                    11                                          3                      ⁢                      M                                                                                                            S                    21                                          3                      ⁢                      M                                                                                                            S                    12                                          3                      ⁢                      M                                                                                                            S                    22                                          3                      ⁢                      M                                                                                                                                  (                                              S                        11                                                  3                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        21                                                  3                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        12                                                  3                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        22                                                  3                          ⁢                          M                                                                    )                                        2                                                                                                              S                      11                                              3                        ⁢                        M                                                              ⁢                                          S                      21                                              3                        ⁢                        M                                                                                                                                                        S                      11                                              3                        ⁢                        M                                                              ⁢                                          S                      12                                              3                        ⁢                        M                                                                                                                                                        S                      11                                              3                        ⁢                        M                                                              ⁢                                          S                      22                                              3                        ⁢                        M                                                                                                                                                        S                      21                                              3                        ⁢                        M                                                              ⁢                                          S                      12                                              3                        ⁢                        M                                                                                                                                                        S                      21                                              3                        ⁢                        M                                                              ⁢                                          S                      22                                              3                        ⁢                        M                                                                                                                                                        S                      12                                              3                        ⁢                        M                                                              ⁢                                          S                      22                                              3                        ⁢                        M                                                                                                              1                                                                                                  S                    11                                          4                      ⁢                      M                                                                                                            S                    21                                          4                      ⁢                      M                                                                                                            S                    12                                          4                      ⁢                      M                                                                                                            S                    22                                          4                      ⁢                      M                                                                                                                                  (                                              S                        11                                                  4                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        21                                                  4                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        12                                                  4                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        22                                                  4                          ⁢                          M                                                                    )                                        2                                                                                                              S                      11                                              4                        ⁢                        M                                                              ⁢                                          S                      21                                              4                        ⁢                        M                                                                                                                                                        S                      11                                              4                        ⁢                        M                                                              ⁢                                          S                      12                                              4                        ⁢                        M                                                                                                                                                        S                      11                                              4                        ⁢                        M                                                              ⁢                                          S                      22                                              4                        ⁢                        M                                                                                                                                                        S                      21                                              4                        ⁢                        M                                                              ⁢                                          S                      12                                              4                        ⁢                        M                                                                                                                                                        S                      21                                              4                        ⁢                        M                                                              ⁢                                          S                      22                                              4                        ⁢                        M                                                                                                                                                        S                      12                                              4                        ⁢                        M                                                              ⁢                                          S                      22                                              4                        ⁢                        M                                                                                                              1                                                                                                  S                    11                                          5                      ⁢                      M                                                                                                            S                    21                                          5                      ⁢                      M                                                                                                            S                    12                                          5                      ⁢                      M                                                                                                            S                    22                                          5                      ⁢                      M                                                                                                                                  (                                              S                        11                                                  5                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        21                                                  5                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        12                                                  5                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        22                                                  5                          ⁢                          M                                                                    )                                        2                                                                                                              S                      11                                              5                        ⁢                        M                                                              ⁢                                          S                      21                                              5                        ⁢                        M                                                                                                                                                        S                      11                                              5                        ⁢                        M                                                              ⁢                                          S                      12                                              5                        ⁢                        M                                                                                                                                                        S                      11                                              5                        ⁢                        M                                                              ⁢                                          S                      22                                              5                        ⁢                        M                                                                                                                                                        S                      21                                              5                        ⁢                        M                                                              ⁢                                          S                      12                                              5                        ⁢                        M                                                                                                                                                        S                      21                                              5                        ⁢                        M                                                              ⁢                                          S                      22                                              5                        ⁢                        M                                                                                                                                                        S                      12                                              5                        ⁢                        M                                                              ⁢                                          S                      22                                              5                        ⁢                        M                                                                                                              1                                                                                                  S                    11                                          6                      ⁢                      M                                                                                                            S                    21                                          6                      ⁢                      M                                                                                                            S                    12                                          6                      ⁢                      M                                                                                                            S                    22                                          6                      ⁢                      M                                                                                                                                  (                                              S                        11                                                  6                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        21                                                  6                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        12                                                  6                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        22                                                  6                          ⁢                          M                                                                    )                                        2                                                                                                              S                      11                                              6                        ⁢                        M                                                              ⁢                                          S                      21                                              6                        ⁢                        M                                                                                                                                                        S                      11                                              6                        ⁢                        M                                                              ⁢                                          S                      12                                              6                        ⁢                        M                                                                                                                                                        S                      11                                              6                        ⁢                        M                                                              ⁢                                          S                      22                                              6                        ⁢                        M                                                                                                                                                        S                      21                                              6                        ⁢                        M                                                              ⁢                                          S                      12                                              6                        ⁢                        M                                                                                                                                                        S                      21                                              6                        ⁢                        M                                                              ⁢                                          S                      22                                              6                        ⁢                        M                                                                                                                                                        S                      12                                              6                        ⁢                        M                                                              ⁢                                          S                      22                                              6                        ⁢                        M                                                                                                              1                                                                                                  S                    11                                          7                      ⁢                      M                                                                                                            S                    21                                          7                      ⁢                      M                                                                                                            S                    12                                          7                      ⁢                      M                                                                                                            S                    22                                          7                      ⁢                      M                                                                                                                                  (                                              S                        11                                                  7                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        21                                                  7                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        12                                                  7                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        22                                                  7                          ⁢                          M                                                                    )                                        2                                                                                                              S                      11                                              7                        ⁢                        M                                                              ⁢                                          S                      21                                              7                        ⁢                        M                                                                                                                                                        S                      11                                              7                        ⁢                        M                                                              ⁢                                          S                      12                                              7                        ⁢                        M                                                                                                                                                        S                      11                                              7                        ⁢                        M                                                              ⁢                                          S                      22                                              7                        ⁢                        M                                                                                                                                                        S                      21                                              7                        ⁢                        M                                                              ⁢                                          S                      12                                              7                        ⁢                        M                                                                                                                                                        S                      21                                              7                        ⁢                        M                                                              ⁢                                          S                      22                                              7                        ⁢                        M                                                                                                                                                        S                      12                                              7                        ⁢                        M                                                              ⁢                                          S                      22                                              7                        ⁢                        M                                                                                                              1                                                                                                  S                    11                                          8                      ⁢                      M                                                                                                            S                    21                                          8                      ⁢                      M                                                                                                            S                    12                                          8                      ⁢                      M                                                                                                            S                    22                                          8                      ⁢                      M                                                                                                                                  (                                              S                        11                                                  8                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        21                                                  8                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        12                                                  8                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        22                                                  8                          ⁢                          M                                                                    )                                        2                                                                                                              S                      11                                              8                        ⁢                        M                                                              ⁢                                          S                      21                                              8                        ⁢                        M                                                                                                                                                        S                      11                                              8                        ⁢                        M                                                              ⁢                                          S                      12                                              8                        ⁢                        M                                                                                                                                                        S                      11                                              8                        ⁢                        M                                                              ⁢                                          S                      22                                              8                        ⁢                        M                                                                                                                                                        S                      21                                              8                        ⁢                        M                                                              ⁢                                          S                      12                                              8                        ⁢                        M                                                                                                                                                        S                      21                                              8                        ⁢                        M                                                              ⁢                                          S                      22                                              8                        ⁢                        M                                                                                                                                                        S                      12                                              8                        ⁢                        M                                                              ⁢                                          S                      22                                              8                        ⁢                        M                                                                                                              1                                                                                                  S                    11                                          9                      ⁢                      M                                                                                                            S                    21                                          9                      ⁢                      M                                                                                                            S                    12                                          9                      ⁢                      M                                                                                                            S                    22                                          9                      ⁢                      M                                                                                                                                  (                                              S                        11                                                  9                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        21                                                  9                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        12                                                  9                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        22                                                  9                          ⁢                          M                                                                    )                                        2                                                                                                              S                      11                                              9                        ⁢                        M                                                              ⁢                                          S                      21                                              9                        ⁢                        M                                                                                                                                                        S                      11                                              9                        ⁢                        M                                                              ⁢                                          S                      12                                              9                        ⁢                        M                                                                                                                                                        S                      11                                              9                        ⁢                        M                                                              ⁢                                          S                      22                                              9                        ⁢                        M                                                                                                                                                        S                      21                                              9                        ⁢                        M                                                              ⁢                                          S                      12                                              9                        ⁢                        M                                                                                                                                                        S                      21                                              9                        ⁢                        M                                                              ⁢                                          S                      22                                              9                        ⁢                        M                                                                                                                                                        S                      12                                              9                        ⁢                        M                                                              ⁢                                          S                      22                                              9                        ⁢                        M                                                                                                              1                                                                                                  S                    11                                          10                      ⁢                      M                                                                                                            S                    21                                          10                      ⁢                      M                                                                                                            S                    12                                          10                      ⁢                      M                                                                                                            S                    22                                          10                      ⁢                      M                                                                                                                                  (                                              S                        11                                                  10                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        21                                                  10                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        12                                                  10                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        22                                                  10                          ⁢                          M                                                                    )                                        2                                                                                                              S                      11                                              10                        ⁢                        M                                                              ⁢                                          S                      21                                              10                        ⁢                        M                                                                                                                                                        S                      11                                              10                        ⁢                        M                                                              ⁢                                          S                      12                                              10                        ⁢                        M                                                                                                                                                        S                      11                                              10                        ⁢                        M                                                              ⁢                                          S                      22                                              10                        ⁢                        M                                                                                                                                                        S                      21                                              10                        ⁢                        M                                                              ⁢                                          S                      12                                              10                        ⁢                        M                                                                                                                                                        S                      21                                              10                        ⁢                        M                                                              ⁢                                          S                      22                                              10                        ⁢                        M                                                                                                                                                        S                      12                                              10                        ⁢                        M                                                              ⁢                                          S                      22                                              10                        ⁢                        M                                                                                                              1                                                                                                  S                    11                                          11                      ⁢                      M                                                                                                            S                    21                                          11                      ⁢                      M                                                                                                            S                    12                                          11                      ⁢                      M                                                                                                            S                    22                                          11                      ⁢                      M                                                                                                                                  (                                              S                        11                                                  11                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        21                                                  11                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        12                                                  11                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        22                                                  11                          ⁢                          M                                                                    )                                        2                                                                                                              S                      11                                              11                        ⁢                        M                                                              ⁢                                          S                      21                                              11                        ⁢                        M                                                                                                                                                        S                      11                                              11                        ⁢                        M                                                              ⁢                                          S                      12                                              11                        ⁢                        M                                                                                                                                                        S                      11                                              11                        ⁢                        M                                                              ⁢                                          S                      22                                              11                        ⁢                        M                                                                                                                                                        S                      21                                              11                        ⁢                        M                                                              ⁢                                          S                      12                                              11                        ⁢                        M                                                                                                                                                        S                      21                                              11                        ⁢                        M                                                              ⁢                                          S                      22                                              11                        ⁢                        M                                                                                                                                                        S                      12                                              11                        ⁢                        M                                                              ⁢                                          S                      22                                              11                        ⁢                        M                                                                                                              1                                                                                                  S                    11                                          12                      ⁢                      M                                                                                                            S                    21                                          12                      ⁢                      M                                                                                                            S                    12                                          12                      ⁢                      M                                                                                                            S                    22                                          12                      ⁢                      M                                                                                                                                  (                                              S                        11                                                  12                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        21                                                  12                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        12                                                  12                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        22                                                  12                          ⁢                          M                                                                    )                                        2                                                                                                              S                      11                                              12                        ⁢                        M                                                              ⁢                                          S                      21                                              12                        ⁢                        M                                                                                                                                                        S                      11                                              12                        ⁢                        M                                                              ⁢                                          S                      12                                              12                        ⁢                        M                                                                                                                                                        S                      11                                              12                        ⁢                        M                                                              ⁢                                          S                      22                                              12                        ⁢                        M                                                                                                                                                        S                      21                                              12                        ⁢                        M                                                              ⁢                                          S                      12                                              12                        ⁢                        M                                                                                                                                                        S                      21                                              12                        ⁢                        M                                                              ⁢                                          S                      22                                              12                        ⁢                        M                                                                                                                                                        S                      12                                              12                        ⁢                        M                                                              ⁢                                          S                      22                                              12                        ⁢                        M                                                                                                              1                                                                                                  S                    11                                          13                      ⁢                      M                                                                                                            S                    21                                          13                      ⁢                      M                                                                                                            S                    12                                          13                      ⁢                      M                                                                                                            S                    22                                          13                      ⁢                      M                                                                                                                                  (                                              S                        11                                                  13                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        21                                                  13                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        12                                                  13                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        22                                                  13                          ⁢                          M                                                                    )                                        2                                                                                                              S                      11                                              13                        ⁢                        M                                                              ⁢                                          S                      21                                              13                        ⁢                        M                                                                                                                                                        S                      11                                              13                        ⁢                        M                                                              ⁢                                          S                      12                                              13                        ⁢                        M                                                                                                                                                        S                      11                                              13                        ⁢                        M                                                              ⁢                                          S                      22                                              13                        ⁢                        M                                                                                                                                                        S                      21                                              13                        ⁢                        M                                                              ⁢                                          S                      12                                              13                        ⁢                        M                                                                                                                                                        S                      21                                              13                        ⁢                        M                                                              ⁢                                          S                      22                                              13                        ⁢                        M                                                                                                                                                        S                      12                                              13                        ⁢                        M                                                              ⁢                                          S                      22                                              13                        ⁢                        M                                                                                                              1                                                                                                  S                    11                                          14                      ⁢                      M                                                                                                            S                    21                                          14                      ⁢                      M                                                                                                            S                    12                                          14                      ⁢                      M                                                                                                            S                    22                                          14                      ⁢                      M                                                                                                                                  (                                              S                        11                                                  14                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        21                                                  14                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        12                                                  14                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        22                                                  14                          ⁢                          M                                                                    )                                        2                                                                                                              S                      11                                              14                        ⁢                        M                                                              ⁢                                          S                      21                                              14                        ⁢                        M                                                                                                                                                        S                      11                                              14                        ⁢                        M                                                              ⁢                                          S                      12                                              14                        ⁢                        M                                                                                                                                                        S                      11                                              14                        ⁢                        M                                                              ⁢                                          S                      22                                              14                        ⁢                        M                                                                                                                                                        S                      21                                              14                        ⁢                        M                                                              ⁢                                          S                      12                                              14                        ⁢                        M                                                                                                                                                        S                      21                                              14                        ⁢                        M                                                              ⁢                                          S                      22                                              14                        ⁢                        M                                                                                                                                                        S                      12                                              14                        ⁢                        M                                                              ⁢                                          S                      22                                              14                        ⁢                        M                                                                                                              1                                                                                                  S                    11                                          15                      ⁢                      M                                                                                                            S                    21                                          15                      ⁢                      M                                                                                                            S                    12                                          15                      ⁢                      M                                                                                                            S                    22                                          15                      ⁢                      M                                                                                                                                  (                                              S                        11                                                  15                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        21                                                  15                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        12                                                  15                          ⁢                          M                                                                    )                                        2                                                                                                              (                                              S                        22                                                  15                          ⁢                          M                                                                    )                                        2                                                                                                              S                      11                                              15                        ⁢                        M                                                              ⁢                                          S                      21                                              15                        ⁢                        M                                                                                                                                                        S                      11                                              15                        ⁢                        M                                                              ⁢                                          S                      12                                              15                        ⁢                        M                                                                                                                                                        S                      11                                              15                        ⁢                        M                                                              ⁢                                          S                      22                                              15                        ⁢                        M                                                                                                                                                        S                      21                                              15                        ⁢                        M                                                              ⁢                                          S                      12                                              15                        ⁢                        M                                                                                                                                                        S                      21                                              15                        ⁢                        M                                                              ⁢                                          S                      22                                              15                        ⁢                        M                                                                                                                                                        S                      12                                              15                        ⁢                        M                                                              ⁢                                          S                      22                                              15                        ⁢                        M                                                                                                              1                                                      )                    ⁢                      (                                                                                d                    1                                                                                                                    d                    2                                                                                                                    d                    3                                                                                                                    d                    4                                                                                                                    d                    5                                                                                                                    d                    6                                                                                                                    d                    7                                                                                                                    d                    8                                                                                                                    d                    9                                                                                                                    d                    10                                                                                                                    d                    11                                                                                                                    d                    12                                                                                                                    d                    13                                                                                                                    d                    14                                                                                                                    d                    0                                                                        )                              
S11p*, S21p*, S12p*, and S22p*: the S parameter of the correction-data acquisition samples measured by the reference measuring system
S11pM, S21pM, S12pM, and S22pM: the S parameter of the correction-data acquisition samples measured by the actual measuring system                               [                      Numerical            ⁢                          xe2x80x83                        ⁢            Formula            ⁢                          xe2x80x83                        ⁢            7                    ]                ⁢                  xe2x80x83                                    xe2x80x83                                          S          11          *                =                              (                                                                                a                    1                                                                                        a                    2                                                                                        a                    3                                                                                        a                    4                                                                                        a                    5                                                                                        a                    6                                                                                        a                    7                                                                                        a                    8                                                                                        a                    9                                                                                        a                    10                                                                                        a                    11                                                                                        a                    12                                                                                        a                    13                                                                                        a                    14                                                                                        a                    0                                                                        )                    ⁢                      (                                                                                S                    11                    M                                                                                                                    S                    21                    M                                                                                                                    S                    12                    M                                                                                                                    S                    22                    M                                                                                                                                          (                                              S                        11                        M                                            )                                        2                                                                                                                                          (                                              S                        21                        M                                            )                                        2                                                                                                                                          (                                              S                        12                        M                                            )                                        2                                                                                                                                          (                                              S                        22                        M                                            )                                        2                                                                                                                                          S                      11                      M                                        ⁢                                          S                      21                      M                                                                                                                                                              S                      11                      M                                        ⁢                                          S                      12                      M                                                                                                                                                              S                      11                      M                                        ⁢                                          S                      22                      M                                                                                                                                                              S                      21                      M                                        ⁢                                          S                      12                      M                                                                                                                                                              S                      21                      M                                        ⁢                                          S                      22                      M                                                                                                                                                              S                      12                      M                                        ⁢                                          S                      22                      M                                                                                                                    1                                                      )                                      C2a                                    [                      Numerical            ⁢                          xe2x80x83                        ⁢            Formula            ⁢                          xe2x80x83                        ⁢            8                    ]                ⁢                  xe2x80x83                                    xe2x80x83                                          S          21          *                =                              (                                                                                b                    1                                                                                        b                    2                                                                                        b                    3                                                                                        b                    4                                                                                        b                    5                                                                                        b                    6                                                                                        b                    7                                                                                        b                    8                                                                                        b                    9                                                                                        b                    10                                                                                        b                    11                                                                                        b                    12                                                                                        b                    13                                                                                        b                    14                                                                                        b                    0                                                                        )                    ⁢                      (                                                                                S                    11                    M                                                                                                                    S                    21                    M                                                                                                                    S                    12                    M                                                                                                                    S                    22                    M                                                                                                                                          (                                              S                        11                        M                                            )                                        2                                                                                                                                          (                                              S                        21                        M                                            )                                        2                                                                                                                                          (                                              S                        12                        M                                            )                                        2                                                                                                                                          (                                              S                        22                        M                                            )                                        2                                                                                                                                          S                      11                      M                                        ⁢                                          S                      21                      M                                                                                                                                                              S                      11                      M                                        ⁢                                          S                      12                      M                                                                                                                                                              S                      11                      M                                        ⁢                                          S                      22                      M                                                                                                                                                              S                      21                      M                                        ⁢                                          S                      12                      M                                                                                                                                                              S                      21                      M                                        ⁢                                          S                      22                      M                                                                                                                                                              S                      12                      M                                        ⁢                                          S                      22                      M                                                                                                                    1                                                      )                                      C2b                                    [                      Numerical            ⁢                          xe2x80x83                        ⁢            Formula            ⁢                          xe2x80x83                        ⁢            9                    ]                ⁢                  xe2x80x83                                    xe2x80x83                                          S          12          *                =                              (                                                                                c                    1                                                                                        c                    2                                                                                        c                    3                                                                                        c                    4                                                                                        c                    5                                                                                        c                    6                                                                                        c                    7                                                                                        c                    8                                                                                        c                    9                                                                                        c                    10                                                                                        c                    11                                                                                        c                    12                                                                                        c                    13                                                                                        c                    14                                                                                        c                    0                                                                        )                    ⁢                      (                                                                                S                    11                    M                                                                                                                    S                    21                    M                                                                                                                    S                    12                    M                                                                                                                    S                    22                    M                                                                                                                                          (                                              S                        11                        M                                            )                                        2                                                                                                                                          (                                              S                        21                        M                                            )                                        2                                                                                                                                          (                                              S                        12                        M                                            )                                        2                                                                                                                                          (                                              S                        22                        M                                            )                                        2                                                                                                                                          S                      11                      M                                        ⁢                                          S                      21                      M                                                                                                                                                              S                      11                      M                                        ⁢                                          S                      12                      M                                                                                                                                                              S                      11                      M                                        ⁢                                          S                      22                      M                                                                                                                                                              S                      21                      M                                        ⁢                                          S                      12                      M                                                                                                                                                              S                      21                      M                                        ⁢                                          S                      22                      M                                                                                                                                                              S                      12                      M                                        ⁢                                          S                      22                      M                                                                                                                    1                                                      )                                      C2c                                    [                      Numerical            ⁢                          xe2x80x83                        ⁢            Formula            ⁢                          xe2x80x83                        ⁢            10                    ]                ⁢                  xe2x80x83                                    xe2x80x83                                          S          22          *                =                              (                                                                                d                    1                                                                                        d                    2                                                                                        d                    3                                                                                        d                    4                                                                                        d                    5                                                                                        d                    6                                                                                        d                    7                                                                                        d                    8                                                                                        d                    9                                                                                        d                    10                                                                                        d                    11                                                                                        d                    12                                                                                        d                    13                                                                                        d                    14                                                                                        d                    0                                                                        )                    ⁢                      (                                                                                S                    11                    M                                                                                                                    S                    21                    M                                                                                                                    S                    12                    M                                                                                                                    S                    22                    M                                                                                                                                          (                                              S                        11                        M                                            )                                        2                                                                                                                                          (                                              S                        21                        M                                            )                                        2                                                                                                                                          (                                              S                        12                        M                                            )                                        2                                                                                                                                          (                                              S                        22                        M                                            )                                        2                                                                                                                                          S                      11                      M                                        ⁢                                          S                      21                      M                                                                                                                                                              S                      11                      M                                        ⁢                                          S                      12                      M                                                                                                                                                              S                      11                      M                                        ⁢                                          S                      22                      M                                                                                                                                                              S                      21                      M                                        ⁢                                          S                      12                      M                                                                                                                                                              S                      21                      M                                        ⁢                                          S                      22                      M                                                                                                                                                              S                      12                      M                                        ⁢                                          S                      22                      M                                                                                                                    1                                                      )                                      C2d      
S11*, S21*, S12*, and S22*: the S parameter of the target electronic component assumed to be obtained by the reference measuring system
S11M, S21M, S12M, and S22M: the S parameter of the target electronic component measured by the actual measuring system
The measurement error correction method according to the present invention may be perfectly applied to the quality checking method of electronic components. In this case, in the quality checking method of to electronic components, a target electronic component with required electrical characteristics to be measured by a reference measuring system is measured by an actual measuring system with a measured result not agreeing with that measured by the reference measuring system so as to check quality based on the measured result.
In the checking method according to the present invention, the electrical characteristics of the target electronic component measured by the actual measuring system are corrected using the measurement error correction method according to the present invention, and then, the target electronic component may be checked by comparing the corrected electrical characteristics with the required electrical characteristics. Thereby, quality of the target electronic component can be checked with high accuracy.
According to the present invention, the following electronic component characteristic measuring system may be proposed as a measuring system capable of performing the measurement error correction method described above.
A measuring system of electronic component characteristics comprises measuring means for measuring electrical characteristics of a target electronic component, measured results of the measuring means do not agree with a reference measuring system; storing means for storing electrical characteristics, which are measured by the reference measuring system, of a correction-data acquisition sample generating the same electrical characteristics as arbitrary electrical characteristics of the target electronic component; interrelating formula computing means for computing an interrelating formula between the electrical characteristics of the correction-data acquisition sample, which are measured by the measuring means, and the electrical characteristics of the correction-data acquisition sample, which are measured by the reference measuring system and stored in the storing means; and correcting means for correcting the electrical characteristics of the target electronic component to electrical characteristics assumed to be obtained by the reference measuring system by substituting the electrical characteristics of the target electronic component measured by the measuring means in the interrelating formula for computation.
When the measuring system according to the present invention is configured based on the analytical relative correction method, the interrelating formula computing means may preferably comprise assuming means for assuming signal transfer patterns of both the measuring systems during measurement to include measurement error factors; creating means for creating a theoretical equation for obtaining a measurement true value of the actual measuring system in the signal transfer pattern and creating a theoretical equation for obtaining a measurement true value of the reference measuring system in the signal transfer pattern; creating means for creating the interrelating formula comprising an arithmetic expression, which includes an undetermined coefficient and directly and exclusively shows the relationship between the measurement true value of the actual measuring system and the measurement true value of the reference measuring system, based on both the theoretical equations; measuring means for measuring electrical characteristics of the correction-data acquisition sample by the reference measuring system and the actual measuring system, respectively; and identifying means for identifying the undetermined coefficient by substituting the electrical characteristics of the correction-data acquisition sample measured by both the measuring systems in the interrelating formula.
When the measuring system according to the present invention is configured based on the approximate relative correction method, the interrelating formula computing means may preferably comprise creating means for creating the interrelating formula comprising an expression of degree n (n is a natural number), which includes an undetermined coefficient and approximately shows the relationship between the value measured by the actual measuring system and the value measured by the reference measuring system; measuring means for measuring electrical characteristics of the correction-data acquisition sample by the reference measuring system and the actual measuring system, respectively; and identifying means for identifying the undetermined coefficient by substituting the electrical characteristics of the correction-data acquisition sample measured by both the measuring systems in the interrelating formula.
According to the present invention, in correcting results measured by the actual measuring system to results measured by the reference measuring system, the correction is performed not by a conventional absolute correction method but by the relative correction method. The relative correction method is a method as follows.
The relative correction method is a method for correcting the electric characteristics (sample true value+measurement errors of the actual measuring system) of a target electronic component measured by the actual measuring system (including actual measurement fixture) to the electric characteristics (sample true value+measurement errors of the reference measuring system) assumed to be obtained by the reference measuring system (including reference measurement fixture). The relative correction method has a feature that the sample true value of a target electronic component is not limited to be known but may be unknown.
The present invention proposes the analytical relative correction method and the approximate relative correction method as a relative correction method. During correction by the analytical relative correction method, a signal transfer pattern including measurement error factors of both the measuring systems should be assumed. In this case, the signal transfer pattern may enough correspond to the measurement error factor, so that it is assumed to be arbitrary one. For such a signal transfer pattern, conventional ones used in the absolute correction method may be employed. The analytical relative correction method can correct the entire linear errors with high accuracy in principle. However, the analytical relative correction method cannot correct nonlinear errors. Such features of the analytical relative correction method are the same as those of the absolute correction method.
The approximate relative correction method is a correction method using an approximate equation instead of the analytical equation when the analytical equation becomes too complicated. In the approximate relative correction method, additional errors cannot be avoided because approximate accuracy of the approximate equation absolutely has the limit. However, the number of the correction-data acquisition samples can be reduced in the approximate relative correction method. Also, it can correct nonlinear errors.
As described above, according to the present invention, measured results, which do not agree with the reference measuring system accurately, can be corrected equally to the results measured by the reference measuring system.
Other features and advantages of the present invention will become apparent from the following description of the invention which refers to the accompanying drawings.